Corpus ID: 237571382

Amplitude equations for SPDEs driven by fractional additive noise with small Hurst parameter

@inproceedings{Blomker2021AmplitudeEF,
  title={Amplitude equations for SPDEs driven by fractional additive noise with small Hurst parameter},
  author={Dirk Blomker and Alexandra Neamtu},
  year={2021}
}
We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter H ∈ (0, 1). Close to a change of stability measured with a small parameter ε, we rely on the natural separation of time-scales and establish a simplified description of the essential dynamics. We prove that up to an error term bounded by a power of ε depending on the Hurst parameter we can approximate the solution of the SPDE in first order by an SDE, the so called… Expand
1 Citations
Center Manifolds for Rough Partial Differential Equations
We prove a center manifold theorem for rough partial differential equations (rough PDEs). The class of rough PDEs we consider contains as a key subclass reaction-diffusion equations driven byExpand

References

SHOWING 1-10 OF 32 REFERENCES
The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations
This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a generalExpand
Modulation and amplitude equations on bounded domains for nonlinear SPDEs driven by cylindrical {\alpha}-stable L\'evy processes
In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical α-stable Lévy processes via modulation or amplitude equations.Expand
Modulation Equation and SPDEs on Unbounded Domains
We consider the approximation via modulation equations for nonlinear SPDEs on unbounded domains with additive space time white noise. Close to a bifurcation an infinite band of eigenvalues changesExpand
Amplitude equations for SPDEs with cubic nonlinearities
For a quite general class of stochastic partial differential equations with cubic nonlinearities, we derive rigorously amplitude equations describing the essential dynamics using the naturalExpand
Stochastic evolution equations with Volterra noise
Volterra processes are continuous stochastic processes whose covariance function can be written in the form R(s,t)=∫0s∧tK(s,r)K(t,r)dr, where K is a suitable square integrable kernel. Examples ofExpand
Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion
We analyze the effect of additive fractional noise with Hurst parameter $$H > {1}/{2}$$ H > 1 / 2 on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach byExpand
FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES
In this paper, stochastic differential equations in a Hilbert space with a standard, cylindrical fractional Brownian motion with the Hurst parameter in the interval (1/2,1) are investigated.Expand
Local mild solutions for rough stochastic partial differential equations
We investigate mild solutions for stochastic evolution equations driven by a fractional Brownian motion (fBm) with Hurst parameter H in (1/3, 1/2] in infinite-dimensional Banach spaces. UsingExpand
Integration with respect to fractal functions and stochastic calculus. I
Abstract. The classical Lebesgue–Stieltjes integral ∫bafdg of real or complex-valued functions on a finite interval (a,b) is extended to a large class of integrands f and integrators g of unboundedExpand
Stochastic evolution equations with fractional Brownian motion
Abstract.In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence andExpand
...
1
2
3
4
...